nLab
large volume limit

Contents

Idea

In Riemannian geometry given any function/functional on the space of Riemannian metrics gg on some manifold XX, then its large volume limit is, if it exists, the limit of the functional evaluated on a sequence tgt g of metrics as tt \to \infty.

This plays a role in particular in the studies of sigma-model quantum field theory with target space (X,g)(X,g). Here the large volume limit may equivalently be thought of as the limit in which the extension of the brane described by the σ\sigma-model vanishes.

One example is the Witten genus, which is the large volume limit of the partition function of the superstring σ\sigma-model (Witten 87, p. 4)

References

  • Edward Witten, Elliptic Genera And Quantum Field Theory , Commun.Math.Phys. 109 525 (1987) (Euclid)

Revised on March 12, 2014 10:15:23 by Urs Schreiber (82.113.98.98)